Let now \(T\)  be a skew projection on \(\mathcal {H}\) . We assume that \(T\)  is genuinely skew, which
is equivalent to the requirement that \(\Vert T\Vert >1\) . Denote by \(P=P_{{\rm Ran}\,T}\)  the orthogonal projection onto
the range of \(T\)  and by \(Q=P_{{\rm Ker}\,T}\)  the orthogonal projection onto the kernel of \(T\) . Afriat [1]}
(see also [2]}) showed that then \(\Vert PQ\Vert < 1\)  and
\(T =(I-PQ)^{-1}P(I-PQ).  \) 
